I'm going to university in a few months and was looking to invest any weekly surplus (£50-75) from my student loan into an index fund.
Most funds appreciate in value by about 7% a year on average after costs, so over the course of a 39 week academic year, I should get approximately 2.514% profit on what I've invested.
By the time the next year starts, this should increase to 4.263%, and, thus, by the time my course finishes 4 years later, I would have 15.73% more than I invested. Obviously, I'm not expecting to beat the interest, but this should hopefully reduce its impact.
Unfortunately, there's a big problem: Every single brokerage I have come across (in the UK) charges a flat fee rather than a percentage (usually that's a good thing, but paying a £12 fee when I'm only investing £75 is a bit much) and, worse yet, none of them allow me to buy 'fractional' shares.
I know Vanguard and some other firms tend to reinvest dividends by buying fractional shares, but these firms only seem to offer managed accounts (with considerable minimum investments and fees in excess of 0.22% of the entire account's balance)
Are there any brokerages that offer trades with a fee that's a percentage of the amount invested and offer 'fractional' shares? Is the cost of making more frequent investments likely to outweigh the compound interest advantage?
: Assuming the 7% figure comes as a result of compound interest, we can take the weekly interest (w) to be the 52nd root of 1.07. This number can then be used as the common ratio of a geometric series with 39 terms. The sum of these terms is given by (1 - w39)/(1-w), so the effective interest is then ((1 - w39)/(1-w))/39 - 1 = 0.02514
: Using our value of 1.02514 from the previous calculation, we can calculate the profit over the remaining 13 weeks of the year by using the compound interest formula: 1.02514 * w13 - 1 = 0.04263
: At a rate of 4.263% per year, an investment of £1 a week yields £40.66. This will earn 7% interest per year, so it too forms a geometric series, and thus the sum of the first 4 terms is given by 40.66 * (1 - 1.074)/(1-0.7) = 180.539. So an investment of £1 * 39 * 4 = £156 yields £180.539 for a profit of £24.539 or 15.73%
: Making 13 investments a year instead of 39 would yield a profit of 15.58%, making 3 a year would yield 14.83%, and investing the money at the end of each academic year would yield 12.89%. This makes me think investing every three weeks may be the optimal strategy to reduce the need for 'fractional' shares (£225 can buy three FTSE-100 tracking ETFs at the moment), whilst also minimizing fees if paying a fixed rate.